Wonders of math

hi ,
i recently found while playing around with my new calculator that any number repeated six times is divisible by 7 ....
for eg, 4 repeated 6 times gives 444444/7 =63492
an say 761 repeated 6 times 761761761761761761/ 7 =108823108823108823
the last one was done using a computer ...
can anyone plz help me out why this happens???

hi ,
repeating an integer, x (say), six times is not the same as multiplying it six times ....
i m sorry but i think u havent got my question correctly...
it is like this
suppose x is an n digit number
repeating it 6 times gives a number
y= 1*x + 10^(n)*x + 10^(2n)*x + 10^(3n)*x+ ....+10^(6n)*x
which is not equal to x^6
and i think i have got the solution for this problem....
if u want me to post it plz tell me , or if u want to find it urself then its good for u

So, a single digit repeated 6 times will always divide by 7 to an integer. In other words, if you multiply 15873 * 7 * n , where n is a single digit, then you will get a number that is that digit repeated 6 times.

If you feel like it, you can attempt similar proofs for more than one digit to see if it holds for more than one digit repeated, and if not than maybe you can find certain conditions for which it would hold with bigger numbers.

hi ,
repeating an integer, x (say), six times is not the same as multiplying it six times ....
i m sorry but i think u havent got my question correctly...
it is like this
suppose x is an n digit number
repeating it 6 times gives a number
y= 1*x + 10^(n)*x + 10^(2n)*x + 10^(3n)*x+ ....+10^(6n)*x
which is not equal to x^6
and i think i have got the solution for this problem....
if u want me to post it plz tell me , or if u want to find it urself then its good for u

regards
Mahesh

You do realize this post doesn't make much sense, do you? First, the person you responded to didn't multiple a number 6 times, he/she did what you did, and just repeated one.

Either you or I have made a mistake, then, Zurtex. Now, if there truly were counter examples, then there would be a smaller on than the one you've just written. Incidentally, what is the remainder of that number mod 7?

As for dividing by 9.

suppose x/9 = y in the integers, then x=9y, and x=9y mod any integer, n say. If 9 and n are relativeyl prime then there is an integer k such that 9k=1 mod n thus xk=y mod n. 9 is a unit modulo 9, 9 is invertible. If 9 and 7 weren't coprime then I couldn't do this.

hai ,
u ppl were right.... when i found one of the solutions for the problem ... i thought it was quite an easy one ... and u rightly pointed out the mistake i made in the formula ...
i apologize for anything from my side...

This cannot be called a proof....
i noted that (1/7) = 0.142857142857142857..... with '142857' reccuring so
y= 1*x + 10^(n)*x + 10^(2n)*x + 10^(3n)*x+ 10^(4n)*x +10^(5n)*x
=x(1+10^n+10^2n+10^3n+10^4n+10^5n)
Now i multiplied both sides with 0.142857142857.....
and found that RHS is always an integer irrespective of the values of x and hence n.
thank u guys for helping me